/usr/share/doc/axiom-doc/hypertex/linconversion.xhtml

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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Conversion</div>
  <hr/>
Conversion is the process of changing an object of one type into an
object of another type. The syntax for conversion is object::newType.
<hr/>
By default, 3 has the type
<a href="db.xhtml?PositiveInteger">PositiveInteger</a>
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="3" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
We can change thisinto an object of type 
<a href="db.xhtml?Fraction(Integer)">Fraction Integer</a> by using "::".
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="makeRequest('p2');"
    value="3::Fraction Integer" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
A coercion is a special kind of conversion that Axiom is allowed to do
automatically when you enter an expression. Coercions are usually 
somewhat safer than more general conversions. The Axiom library contains
operations called 
<a href="dbopcoerce.xhtml">coerce</a> and
<a href="dbopconvert.xhtml">convert</a>. Only the
<a href="dbopcoerce.xhtml">coerce</a> operations can be used by the
interpreter to change an object into an object of another type unless
you explicitly use a "::".

By now you will be quite familiar with what types and modes look like.
It is useful to think of a type or mode as a pattern for what you want
the result to be. Let's start with a square matrix of polynomials with
complex rational number coefficients.
<ul>
 <li>
  <input type="submit" id="p3" class="noresult" 
    onclick="makeRequest('p3');"
    value="m:SquareMatrix(2,POLY COMPLEX FRAC INT)" />
  <div id="ansp3"><div></div></div>
 </li>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="handleFree(['p3','p4']);"
    value="m:=matrix [ [x-3/4*%i,z*y^2+1/2],[3/7*%i*y^4-x,12-%i*9/5]]" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
We first want to interchange the <a href="db.xthml?Complex">Complex</a>
and <a href="db.xhtml?Fraction">Fraction</a> layers. We do the conversion
by doing the interchange in the type expression.
<ul>
 <li>
  <input type="submit" id="p5" class="subbut" 
    onclick="handleFree(['p3','p4','p5']);"
    value="m1:=m::SquareMatrix(2,POLY FRAC COMPLEX INT)" />
  <div id="ansp5"><div></div></div>
 </li>
</ul>
Interchange the <a href="db.xhtml?Polynomial">Polynomial</a> and the
<a href="db.xhtml?Fraction">Fraction</a> levels.
<ul>
 <li>
  <input type="submit" id="p6" class="subbut" 
    onclick="handleFree(['p3','p4','p5','p6']);"
    value="m2:=m1::SquareMatrix(2,FRAC POLY COMPLEX INT)" />
  <div id="ansp6"><div></div></div>
 </li>
</ul>
Interchange the <a href="db.xhtml?Polynomial">Polynomial</a> and the
<a href="db.xhtml?Complex">Complex</a> levels.
<ul>
 <li>
  <input type="submit" id="p7" class="subbut" 
    onclick="handleFree(['p3','p4','p5','p6','p7']);"
    value="m3:=m2::SquareMatrix(2,FRAC COMPLEX POLY INT)" />
  <div id="ansp7"><div></div></div>
 </li>
</ul>
All the entries have changed types, although in comparing the last two
results only the entry in the lower left corner looks different. We did
all the intermediate steps to show you what Axiom can do.

In fact, we could have combined all these into one conversion.
<ul>
 <li>
  <input type="submit" id="p8" class="subbut" 
    onclick="handleFree(['p3','p4','p8']);"
    value="m::SquareMatrix(2,FRAC COMPLEX POLY INT)" />
  <div id="ansp8"><div></div></div>
 </li>
</ul>

There are times when Axiom is not able to do the conversion in one step.
You may need to break up the transformation into several conversions in 
order to get an object of the desired type.

We cannot move either the <a href="db.xhtml?Fraction">Fraction</a> or
<a href="db.xhtml?Complex">Complex</a> above (or to the left of,
depending on how you look at it) 
<a href="db.xhtml?SquareMatrix">SquareMatrix</a> because each of these
levels requires that its argument type have commutative multiplication,
whereas <a href="db.xhtml?SquareMatrix">SquareMatrix</a> does not.
(<a href="db.xhtml?Fraction">Fraction</a> requires that its argument 
belong to the category 
<a href="db.xhtml?IntegralDomain">IntegralDomain</a> and 
<a href="db.xhtml?Complex">Complex</a> requires that its argument belongs to
<a href="db.xhtml?CommutativeRing">CommutativeRing</a>. See the
<a href="axbook/section-2.1.xhtml">Jenks section 2.1</a> for a brief
discussion of categories. The <a href="db.xhtml?Integer">Integer</a> level
did not move anywhere because it does not allow any arguments. We also did
not move the <a href="db.xhtml?SquareMatrix">SquareMatrix</a> part
anywhere, but we could have. Recall that m looks like this:
<ul>
 <li>
  <input type="submit" id="p9" class="subbut" 
    onclick="handleFree(['p3','p4','p9']);"
    value="m" />
  <div id="ansp9"><div></div></div>
 </li>
</ul>
If we want a polynomial with matrxi coefficients rather than a matrix with
polynomial entries, we can just do the conversion.
<ul>
 <li>
  <input type="submit" id="p10" class="subbut" 
    onclick="handleFree(['p3','p4','p10']);"
    value="m::POLY SquareMatrix(2,COMPLEX FRAC INT)" />
  <div id="ansp10"><div></div></div>
 </li>
</ul>
We have not yet used modes for any conversions. Modes are a great 
shorthand for indicating the type of the object you want. Instead of
using the long type expression in the last example we could have 
simply said this:
<ul>
 <li>
  <input type="submit" id="p11" class="subbut" 
    onclick="handleFree(['p3','p4','p11']);"
    value="m::POLY ?" />
  <div id="ansp11"><div></div></div>
 </li>
</ul>
We can also indicate more structure if we want the entries of the matrices
to be fractions.
<ul>
 <li>
  <input type="submit" id="p12" class="subbut" 
    onclick="handleFree(['p3','p4','p12']);"
    value="m::POLY SquareMatrix(2,FRAC ?)" />
  <div id="ansp12"><div></div></div>
 </li>
</ul>
 </body>
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / linconversion.xhtml
